There were violent clashes in Rome at the weekend as thousands protested moves to extend Italy's COVID pass to all workplaces from October 15.
A dozen people were detained or arrested following the demonstration on Saturday, including the leaders of the far-right Forza Nuova party, Giuliano Castellino and Roberto Fiore.
The party members have been accused of stoking tension and violence.
Although the march was authorised, it saw demonstrators confront the police and wreck the headquarters of the Italian General Confederation of Labour (CGIL), a trade union.
A number of photos and videos have emerged of mostly male protestors giving fascist salutes.
On Sunday left-leaning Italian lawmakers and politicians called for measures to outlaw pro-fascism groups
To get the certification, known as a "Green Pass" in Italy, residents must either have had at least one coronavirus vaccine dose, proof of recovery from the illness in the last six months, or a negative test in the previous 48 hours.
Any employees refusing to comply face suspension without pay. The system is already in place for all medical staff and in schools.
Prime Minister Mario Draghi condemned the violence and said the government would continue its commitment to complete the vaccination campaign against COVID-19.
Nearly 80% of the over-12s in Italy have been fully vaccinated, according to government statistics.